Solid state (Space Lattice and Unit cell)

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Solid state (Space Lattice and Unit cell):

Space Lattice and unit cell:
 A space  lattice is an array of points showing how molecules, atoms or ion are arranged at different sites in three-dimensional space . 
      A unit cell is the smallest repeating unit in space lattice which when repeated over and over again result in a crystal of the given substance.

Seven Crystal systems:


 Bravais Lattices:
14 type of bravais lattice .

Q)Calculate the number of atom contained within 1) a primitive cubic unit ,2) a body-centred(b.c.c) unit cell ,3) a face-centred cubic (f.c.c) unit cell .
Ans:
1) The primitive cubic unit cell consists of one atom at each of the 8 corners.Each atom is thus shared by 8 unit .Hence, n=8*1/8=1
2) The b.c.c unit consists of 8 atoms at the 8 corners and one atom at the centre .At each cornee only 1/8th of the atom is within the unit cell. thus , the contribution of the 8 corner is 8*1/8=1 while body-centred atom is 1 hence, n=1+1=2

3) The 8 atoms at the corners contribute 8*1/8=1. There is one atom at each of the 6 face , Which is shared by 2 unit cells each  , therefore,the contribution of 6 face-centred atoms=

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